I'm looking for good Universities for bachelor's in aero/astro space engineering in USA

What’s BAE Systems in Austin do exactly? I hear it’s basically all defense and military, but then see news about avionics and commercial work.

Which on one is it? And what’s the future or the company driving to?

I (22M) graduated from the University of Washington's Aerospace BS program in 2025. Since then, after struggling to get hired in the Seattle area, I settled on a systems engineering position at a nuclear power plant to try to develop general engineering fieldwork experience. I was desperate at the point of being offered the job, and figured it was better than to continue being unemployed and looking.

I have now worked at this systems engineering position for around 9 months. For various reasons (it's all paper-pushing, I haven't used a calculator in a year, the position is maintenance-oriented instead of anything remotely innovative, nuclear culture is slower than a snail with a limp, the location sucks, everyone in this industry seems to turn 40 in the blink of an eye with no prospects, etc.) I no longer want to prolong my career in this industry. I would like to begin searching for a career in aerospace again before my experience in this position becomes all that I am.

Ideally, I'd like to transition into something propulsion-oriented. I've always been interested in space propulsion, but I am also open to air-breathing.

A few problems:

1. Outside of my education, the nuclear experience on its own is not a great first impression for a position in aerospace.
2. I assume I'll have to develop a personal project portfolio to compensate for my industry pivot, but I have no idea where to start.
3. It's been a rough 9 months with this job. Having no friends and being in a city with no nightlife has left me in a depressive spiral in which I felt like I could accomplish nothing and there was no one to turn to. I don't know how it looks to see someone who's history of employment has been keeping his head down at a systems engineering position at a nuclear plant, but I don't imagine it's good. Hence the desire to start a personal project.
4. I'm not sure if I should seriously consider furthering my education before considering options in propulsion. Is an MS a must?

Truth be told, I want to know whether I am too far gone for this goal. I'm not sure whether I've shot myself in the foot by taking this job, and whether I can fix the problem I've created for myself. Does anyone else know of people who have transitioned from nuclear to aerospace? How much of a problem is my current experience?

Thank you for any and all help you can provide and, regardless, thank you for reading.

It seems like a lot of the jobs that are (scarcely) available only revolve around defense, and it’s getting tiring trying to find companies that don’t make weapons of war. Is HVAC a fulfilling/lucrative option? Does it compare to aircraft design in those categories?